Gravitational-wave astronomy

Gravitational-wave astronomy is an emerging field of science, concerning the observations of gravitational waves (minute distortions of spacetime predicted by Albert Einstein's theory of general relativity) to collect relatively unique data and make inferences about objects such as neutron stars and black holes, events such as supernovae, and processes including those of the early universe shortly after the Big Bang.

Data about the first observation of gravitational waves from LIGO and Virgo interferometer

Introduction
Main article: Gravitational wave

Gravitational waves are waves of the intensity of gravity generated by the accelerated masses of an orbital binary system that propagate as waves outward from their source at the speed of light. They were first proposed by Oliver Heaviside in 1893 and then later by Henri Poincaré in 1905 as waves similar to electromagnetic waves but the gravitational equivalent.

Gravitational waves were later predicted in 1916 by Albert Einstein on the basis of his general theory of relativity as ripples in spacetime. Later he refused to accept gravitational waves. Gravitational waves transport energy as gravitational radiation, a form of radiant energy similar to electromagnetic radiation. Newton's law of universal gravitation, part of classical mechanics, does not provide for their existence, since that law is predicated on the assumption that physical interactions propagate instantaneously (at infinite speed) – showing one of the ways the methods of Newtonian physics are unable to explain phenomena associated with relativity.

The first indirect evidence for the existence of gravitational waves came in 1974 from the observed orbital decay of the Hulse–Taylor binary pulsar, which matched the decay predicted by general relativity as energy is lost to gravitational radiation. In 1993, Russell A. Hulse and Joseph Hooton Taylor Jr. received the Nobel Prize in Physics for this discovery.

Direct observation of gravitational waves was not made until 2015, when a signal generated by the merger of two black holes was received by the LIGO gravitational wave detectors in Livingston, Louisiana, and in Hanford, Washington. The 2017 Nobel Prize in Physics was subsequently awarded to Rainer Weiss, Kip Thorne and Barry Barish for their role in the direct detection of gravitational waves.

In gravitational-wave astronomy, observations of gravitational waves are used to infer data about the sources of gravitational waves. Sources that can be studied this way include binary star systems composed of white dwarfs, neutron stars, and black holes; events such as supernovae; and the formation of the early universe shortly after the Big Bang.

Instruments and challenges
Main article: List of gravitational wave observations

Collaboration between detectors aids in collecting unique and valuable information, owing to different specifications and sensitivity of each. There are several ground-based laser interferometers which span several miles/kilometers, including: the two Laser Interferometer Gravitational-Wave Observatory (LIGO) detectors in WA and LA, USA; Virgo, at the European Gravitational Observatory in Italy; GEO600 in Germany, and the Kamioka Gravitational Wave Detector (KAGRA) in Japan. While LIGO, Virgo, and KAGRA have made joint observations to date, GEO600 is currently utilized for trial and test runs, due to lower sensitivity of its instruments, and has not participated in joint runs with the others recently.

Noise curves for a selection of gravitational-wave detectors as a function of frequency. At very low frequencies are pulsar timing arrays, at low frequencies are space-borne detectors, and at high frequencies are ground-based detectors. The characteristic strain of potential astrophysical sources are also shown. To be detectable the characteristic strain of a signal must be above the noise curve.[1]

High frequency

In 2015, the LIGO project was the first to directly observe gravitational waves using laser interferometers.[2][3] The LIGO detectors observed gravitational waves from the merger of two stellar-mass black holes, matching predictions of general relativity.[4][5][6] These observations demonstrated the existence of binary stellar-mass black hole systems, and were the first direct detection of gravitational waves and the first observation of a binary black hole merger.[7] This finding has been characterized as revolutionary to science, because of the verification of our ability to use gravitational-wave astronomy to progress in our search and exploration of dark matter and the big bang.

Low frequency

An alternative means of observation is using pulsar timing arrays (PTAs). There are three consortia, the European Pulsar Timing Array (EPTA), the North American Nanohertz Observatory for Gravitational Waves (NANOGrav), and the Parkes Pulsar Timing Array (PPTA), which co-operate as the International Pulsar Timing Array. These use existing radio telescopes, but since they are sensitive to frequencies in the nanohertz range, many years of observation are needed to detect a signal and detector sensitivity improves gradually. Current bounds are approaching those expected for astrophysical sources.[8]

Plot of correlation between pulsars observed by NANOGrav (2023) vs angular separation between pulsars, compared with a theoretical Hellings-Downs model (dashed purple) and if there were no gravitational wave background (solid green)[9][10]

In June 2023, four PTA collaborations, the three mentioned above and the Chinese Pulsar Timing Array, delivered independent but similar evidence for a stochastic background of nanohertz gravitational waves.[11] Each provided an independent first measurement of the theoretical Hellings-Downs curve, i.e., the quadrupolar correlation between two pulsars as a function of their angular separation in the sky, which is a telltale sign of the gravitational wave origin of the observed background.[12][13][14][15] The sources of this background remain to be identified, although binaries of supermassive black holes are the most likely candidates.[16]

Intermediate frequencies

Further in the future, there is the possibility of space-borne detectors. The European Space Agency has selected a gravitational-wave mission for its L3 mission, due to launch 2034, the current concept is the evolved Laser Interferometer Space Antenna (eLISA).[17] Also in development is the Japanese Deci-hertz Interferometer Gravitational wave Observatory (DECIGO).

Scientific value

Astronomy has traditionally relied on electromagnetic radiation. Originating with the visible band, as technology advanced, it became possible to observe other parts of the electromagnetic spectrum, from radio to gamma rays. Each new frequency band gave a new perspective on the Universe and heralded new discoveries.[18] During the 20th century, indirect and later direct measurements of high-energy, massive, particles provided an additional window into the cosmos. Late in the 20th century, the detection of solar neutrinos founded the field of neutrino astronomy, giving an insight into previously inaccessible phenomena, such as the inner workings of the Sun.[19][20] The observation of gravitational waves provides a further means of making astrophysical observations.

Russell Hulse and Joseph Taylor were awarded the 1993 Nobel Prize in Physics for showing that the orbital decay of a pair of neutron stars, one of them a pulsar, fits general relativity's predictions of gravitational radiation.[21] Subsequently, many other binary pulsars (including one double pulsar system) have been observed, all fitting gravitational-wave predictions.[22] In 2017, the Nobel Prize in Physics was awarded to Rainer Weiss, Kip Thorne and Barry Barish for their role in the first detection of gravitational waves.[23][24][25]

Gravitational waves provide complementary information to that provided by other means. By combining observations of a single event made using different means, it is possible to gain a more complete understanding of the source's properties. This is known as multi-messenger astronomy. Gravitational waves can also be used to observe systems that are invisible (or almost impossible to detect) by any other means. For example, they provide a unique method of measuring the properties of black holes.

Gravitational waves can be emitted by many systems, but, to produce detectable signals, the source must consist of extremely massive objects moving at a significant fraction of the speed of light. The main source is a binary of two compact objects. Example systems include:

  • Compact binaries made up of two closely orbiting stellar-mass objects, such as white dwarfs, neutron stars or black holes. Wider binaries, which have lower orbital frequencies, are a source for detectors like LISA.[26][27] Closer binaries produce a signal for ground-based detectors like LIGO.[28] Ground-based detectors could potentially detect binaries containing an intermediate mass black hole of several hundred solar masses.[29][30]
  • Supermassive black hole binaries, consisting of two black holes with masses of 105–109 solar masses. Supermassive black holes are found at the centre of galaxies. When galaxies merge, it is expected that their central supermassive black holes merge too.[31] These are potentially the loudest gravitational-wave signals. The most massive binaries are a source for PTAs.[32] Less massive binaries (about a million solar masses) are a source for space-borne detectors like LISA.[33]
  • Extreme-mass-ratio systems of a stellar-mass compact object orbiting a supermassive black hole.[34] These are sources for detectors like LISA.[33] Systems with highly eccentric orbits produce a burst of gravitational radiation as they pass through the point of closest approach;[35] systems with near-circular orbits, which are expected towards the end of the inspiral, emit continuously within LISA's frequency band.[36] Extreme-mass-ratio inspirals can be observed over many orbits. This makes them excellent probes of the background spacetime geometry, allowing for precision tests of general relativity.[37]

In addition to binaries, there are other potential sources:

  • Supernovae generate high-frequency bursts of gravitational waves that could be detected with LIGO or Virgo.[38]
  • Rotating neutron stars are a source of continuous high-frequency waves if they possess axial asymmetry.[39][40]
  • Early universe processes, such as inflation or a phase transition.[41]
  • Cosmic strings could also emit gravitational radiation if they do exist.[42] Discovery of these gravitational waves would confirm the existence of cosmic strings.

Gravitational waves interact only weakly with matter. This is what makes them difficult to detect. It also means that they can travel freely through the Universe, and are not absorbed or scattered like electromagnetic radiation. It is therefore possible to see to the center of dense systems, like the cores of supernovae or the Galactic Center. It is also possible to see further back in time than with electromagnetic radiation, as the early universe was opaque to light prior to recombination, but transparent to gravitational waves.[43]

The ability of gravitational waves to move freely through matter also means that gravitational-wave detectors, unlike telescopes, are not pointed to observe a single field of view but observe the entire sky. Detectors are more sensitive in some directions than others, which is one reason why it is beneficial to have a network of detectors.[44] Directionalization is also poor, due to the small number of detectors.

In cosmic inflation

Cosmic inflation, a hypothesized period when the universe rapidly expanded during the first 10−36 seconds after the Big Bang, would have given rise to gravitational waves; that would have left a characteristic imprint in the polarization of the CMB radiation.[45][46]

It is possible to calculate the properties of the primordial gravitational waves from measurements of the patterns in the microwave radiation, and use those calculations to learn about the early universe.

Development
The LIGO Hanford Control Room

As a young area of research, gravitational-wave astronomy is still in development; however, there is consensus within the astrophysics community that this field will evolve to become an established component of 21st century multi-messenger astronomy.[47]

Gravitational-wave observations complement observations in the electromagnetic spectrum.[48][47] These waves also promise to yield information in ways not possible via detection and analysis of electromagnetic waves. Electromagnetic waves can be absorbed and re-radiated in ways that make extracting information about the source difficult. Gravitational waves, however, only interact weakly with matter, meaning that they are not scattered or absorbed. This should allow astronomers to view the center of a supernova, stellar nebulae, and even colliding galactic cores in new ways.

Ground-based detectors have yielded new information about the inspiral phase and mergers of binary systems of two stellar mass black holes, and merger of two neutron stars. They could also detect signals from core-collapse supernovae, and from periodic sources such as pulsars with small deformations. If there is truth to speculation about certain kinds of phase transitions or kink bursts from long cosmic strings in the very early universe (at cosmic times around 10−25 seconds), these could also be detectable.[49] Space-based detectors like LISA should detect objects such as binaries consisting of two white dwarfs, and AM CVn stars (a white dwarf accreting matter from its binary partner, a low-mass helium star), and also observe the mergers of supermassive black holes and the inspiral of smaller objects (between one and a thousand solar masses) into such black holes. LISA should also be able to listen to the same kind of sources from the early universe as ground-based detectors, but at even lower frequencies and with greatly increased sensitivity.[50]

Detecting emitted gravitational waves is a difficult endeavor. It involves ultra-stable high-quality lasers and detectors calibrated with a sensitivity of at least 2·10−22 Hz−1/2 as shown at the ground-based detector, GEO600.[51] It has also been proposed that even from large astronomical events, such as supernova explosions, these waves are likely to degrade to vibrations as small as an atomic diameter.[52]

See also

References
  1. Moore, Christopher; Cole, Robert; Berry, Christopher (19 July 2013). "Gravitational Wave Detectors and Sources". Retrieved 17 April 2014.
  2. Overbye, Dennis (11 February 2016). "Physicists Detect Gravitational Waves, Proving Einstein Right". New York Times. Retrieved 11 February 2016.
  3. Krauss, Lawrence (11 February 2016). "Finding Beauty in the Darkness". New York Times. Retrieved 11 February 2016.
  4. Pretorius, Frans (2005). "Evolution of Binary Black-Hole Spacetimes". Physical Review Letters. 95 (12): 121101. arXiv:gr-qc/0507014. Bibcode:2005PhRvL..95l1101P. doi:10.1103/PhysRevLett.95.121101. ISSN 0031-9007. PMID 16197061. S2CID 24225193.
  5. Campanelli, M.; Lousto, C. O.; Marronetti, P.; Zlochower, Y. (2006). "Accurate Evolutions of Orbiting Black-Hole Binaries without Excision". Physical Review Letters. 96 (11): 111101. arXiv:gr-qc/0511048. Bibcode:2006PhRvL..96k1101C. doi:10.1103/PhysRevLett.96.111101. ISSN 0031-9007. PMID 16605808. S2CID 5954627.
  6. Baker, John G.; Centrella, Joan; Choi, Dae-Il; Koppitz, Michael; van Meter, James (2006). "Gravitational-Wave Extraction from an Inspiraling Configuration of Merging Black Holes". Physical Review Letters. 96 (11): 111102. arXiv:gr-qc/0511103. Bibcode:2006PhRvL..96k1102B. doi:10.1103/PhysRevLett.96.111102. ISSN 0031-9007. PMID 16605809. S2CID 23409406.
  7. Abbott, B. P.; Abbott, R.; Abbott, T. D.; Abernathy, M. R.; Acernese, F.; Ackley, K.; Adams, C.; Adams, T.; Addesso, P. (2016-02-11). "Observation of Gravitational Waves from a Binary Black Hole Merger". Physical Review Letters. 116 (6): 061102. arXiv:1602.03837. Bibcode:2016PhRvL.116f1102A. doi:10.1103/PhysRevLett.116.061102. ISSN 0031-9007. PMID 26918975. S2CID 124959784.
  8. Sesana, A. (22 May 2013). "Systematic investigation of the expected gravitational wave signal from supermassive black hole binaries in the pulsar timing band". Monthly Notices of the Royal Astronomical Society: Letters. 433 (1): L1–L5. arXiv:1211.5375. Bibcode:2013MNRAS.433L...1S. doi:10.1093/mnrasl/slt034. S2CID 11176297.
  9. "IOPscience - Focus on NANOGrav's 15 yr Data Set and the Gravitational Wave Background".
  10. "After 15 years, pulsar timing yields evidence of cosmic gravitational wave background". 29 June 2023.
  11. O'Callaghan, Jonathan (28 June 2023). "An Enormous Gravity 'Hum' Moves Through the Universe". quantamagazine.org. Astronomers have found a background din of exceptionally long-wavelength gravitational waves pervading the cosmos. The cause? Probably supermassive black hole collisions, but more exotic options can't be ruled out.
  12. Agazie, Gabriella; Anumarlapudi, Akash; Archibald, Anne M.; Arzoumanian, Zaven; Baker, Paul T.; Bécsy, Bence; Blecha, Laura; Brazier, Adam; Brook, Paul R.; Burke-Spolaor, Sarah; Burnette, Rand; Case, Robin; Charisi, Maria; Chatterjee, Shami; Chatziioannou, Katerina (June 2023). "The NANOGrav 15 yr Data Set: Evidence for a Gravitational-wave Background". The Astrophysical Journal Letters. 951 (1): L8. arXiv:2306.16213. doi:10.3847/2041-8213/acdac6. ISSN 2041-8205. S2CID 259274684. Archived from the original on 29 June 2023.
  13. Antoniadis, J. (28 June 2023). "The second data release from the European Pulsar Timing Array III. Search for gravitational wave signals". arXiv:2306.16214 [astro-ph.HE].
  14. Reardon, Daniel J.; Zic, Andrew; Shannon, Ryan M.; Hobbs, George B.; Bailes, Matthew; Di Marco, Valentina; Kapur, Agastya; Rogers, Axl F.; Thrane, Eric; Askew, Jacob; Bhat, N. D. Ramesh; Cameron, Andrew; Curyło, Małgorzata; Coles, William A.; Dai, Shi (2023-06-29). "Search for an Isotropic Gravitational-wave Background with the Parkes Pulsar Timing Array". The Astrophysical Journal Letters. 951 (1): L6. arXiv:2306.16215. doi:10.3847/2041-8213/acdd02. ISSN 2041-8205. S2CID 259275121.
  15. Xu, Heng; Chen, Siyuan; Guo, Yanjun; Jiang, Jinchen; Wang, Bojun; Xu, Jiangwei; Xue, Zihan; Nicolas Caballero, R.; Yuan, Jianping; Xu, Yonghua; Wang, Jingbo; Hao, Longfei; Luo, Jingtao; Lee, Kejia; Han, Jinlin (2023-06-29). "Searching for the Nano-Hertz Stochastic Gravitational Wave Background with the Chinese Pulsar Timing Array Data Release I". Research in Astronomy and Astrophysics. 23 (7): 075024. arXiv:2306.16216. doi:10.1088/1674-4527/acdfa5. ISSN 1674-4527. S2CID 259274998.
  16. O'Callaghan, Jonathan (4 August 2023). "A Background 'Hum' Pervades the Universe. Scientists Are Racing to Find Its Source". scientificamerican.com. Retrieved 5 August 2023. Astronomers are now seeking to pinpoint the origins of an exciting new form of gravitational waves that was announced earlier this year.
  17. "ESA's new vision to study the invisible universe". ESA. Retrieved 29 November 2013.
  18. Longair, Malcolm (2012). Cosmic century: a history of astrophysics and cosmology. Cambridge University Press. ISBN 978-1107669369.
  19. Bahcall, John N. (1989). Neutrino Astrophysics (Reprinted. ed.). Cambridge: Cambridge University Press. ISBN 978-0521379755.
  20. Bahcall, John (9 June 2000). "How the Sun Shines". Nobel Prize. Retrieved 10 May 2014.
  21. "The Nobel Prize in Physics 1993". Nobel Foundation. Retrieved 2014-05-03.
  22. Stairs, Ingrid H. (2003). "Testing General Relativity with Pulsar Timing". Living Reviews in Relativity. 6 (1): 5. arXiv:astro-ph/0307536. Bibcode:2003LRR.....6....5S. doi:10.12942/lrr-2003-5. PMC 5253800. PMID 28163640.
  23. Rincon, Paul; Amos, Jonathan (3 October 2017). "Einstein's waves win Nobel Prize". BBC News. Retrieved 3 October 2017.
  24. Overbye, Dennis (3 October 2017). "2017 Nobel Prize in Physics Awarded to LIGO Black Hole Researchers". The New York Times. Retrieved 3 October 2017.
  25. Kaiser, David (3 October 2017). "Learning from Gravitational Waves". The New York Times. Retrieved 3 October 2017.
  26. Nelemans, Gijs (7 May 2009). "The Galactic gravitational wave foreground". Classical and Quantum Gravity. 26 (9): 094030. arXiv:0901.1778. Bibcode:2009CQGra..26i4030N. doi:10.1088/0264-9381/26/9/094030. S2CID 11275836.
  27. Stroeer, A; Vecchio, A (7 October 2006). "The LISA verification binaries". Classical and Quantum Gravity. 23 (19): S809–S817. arXiv:astro-ph/0605227. Bibcode:2006CQGra..23S.809S. doi:10.1088/0264-9381/23/19/S19. S2CID 9338900.
  28. Abadie, J.; et al. (7 September 2010). "Predictions for the rates of compact binary coalescences observable by ground-based gravitational-wave detectors". Classical and Quantum Gravity. 27 (17): 173001. arXiv:1003.2480. Bibcode:2010CQGra..27q3001A. doi:10.1088/0264-9381/27/17/173001. S2CID 15200690.
  29. "Measuring Intermediate-Mass Black-Hole Binaries with Advanced Gravitational Wave Detectors". Gravitational Physics Group. University of Birmingham. Retrieved 28 November 2015.
  30. "Observing the invisible collisions of intermediate mass black holes". LIGO Scientific Collaboration. Retrieved 28 November 2015.
  31. Volonteri, Marta; Haardt, Francesco; Madau, Piero (10 January 2003). "The Assembly and Merging History of Supermassive Black Holes in Hierarchical Models of Galaxy Formation". The Astrophysical Journal. 582 (2): 559–573. arXiv:astro-ph/0207276. Bibcode:2003ApJ...582..559V. doi:10.1086/344675. S2CID 2384554.
  32. Sesana, A.; Vecchio, A.; Colacino, C. N. (11 October 2008). "The stochastic gravitational-wave background from massive black hole binary systems: implications for observations with Pulsar Timing Arrays". Monthly Notices of the Royal Astronomical Society. 390 (1): 192–209. arXiv:0804.4476. Bibcode:2008MNRAS.390..192S. doi:10.1111/j.1365-2966.2008.13682.x. S2CID 18929126.
  33. Amaro-Seoane, Pau; Aoudia, Sofiane; Babak, Stanislav; Binétruy, Pierre; Berti, Emanuele; Bohé, Alejandro; Caprini, Chiara; Colpi, Monica; Cornish, Neil J.; Danzmann, Karsten; Dufaux, Jean-François; Gair, Jonathan; Jennrich, Oliver; Jetzer, Philippe; Klein, Antoine; Lang, Ryan N.; Lobo, Alberto; Littenberg, Tyson; McWilliams, Sean T.; Nelemans, Gijs; Petiteau, Antoine; Porter, Edward K.; Schutz, Bernard F.; Sesana, Alberto; Stebbins, Robin; Sumner, Tim; Vallisneri, Michele; Vitale, Stefano; Volonteri, Marta; Ward, Henry (21 June 2012). "Low-frequency gravitational-wave science with eLISA/NGO". Classical and Quantum Gravity. 29 (12): 124016. arXiv:1202.0839. Bibcode:2012CQGra..29l4016A. doi:10.1088/0264-9381/29/12/124016. S2CID 54822413.
  34. Amaro-Seoane, P. (May 2012). "Stellar dynamics and extreme-mass ratio inspirals". Living Reviews in Relativity. 21 (1): 4. arXiv:1205.5240. Bibcode:2018LRR....21....4A. doi:10.1007/s41114-018-0013-8. PMC 5954169. PMID 29780279.
  35. Berry, C. P. L.; Gair, J. R. (12 December 2012). "Observing the Galaxy's massive black hole with gravitational wave bursts". Monthly Notices of the Royal Astronomical Society. 429 (1): 589–612. arXiv:1210.2778. Bibcode:2013MNRAS.429..589B. doi:10.1093/mnras/sts360. S2CID 118944979.
  36. Amaro-Seoane, Pau; Gair, Jonathan R; Freitag, Marc; Miller, M Coleman; Mandel, Ilya; Cutler, Curt J; Babak, Stanislav (7 September 2007). "Intermediate and extreme mass-ratio inspirals—astrophysics, science applications and detection using LISA". Classical and Quantum Gravity. 24 (17): R113–R169. arXiv:astro-ph/0703495. Bibcode:2007CQGra..24R.113A. doi:10.1088/0264-9381/24/17/R01. S2CID 37683679.
  37. Gair, Jonathan; Vallisneri, Michele; Larson, Shane L.; Baker, John G. (2013). "Testing General Relativity with Low-Frequency, Space-Based Gravitational-Wave Detectors". Living Reviews in Relativity. 16 (1): 7. arXiv:1212.5575. Bibcode:2013LRR....16....7G. doi:10.12942/lrr-2013-7. PMC 5255528. PMID 28163624.
  38. Kotake, Kei; Sato, Katsuhiko; Takahashi, Keitaro (1 April 2006). "Explosion mechanism, neutrino burst and gravitational wave in core-collapse supernovae". Reports on Progress in Physics. 69 (4): 971–1143. arXiv:astro-ph/0509456. Bibcode:2006RPPh...69..971K. doi:10.1088/0034-4885/69/4/R03. S2CID 119103628.
  39. Abbott, B.; et al. (2007). "Searches for periodic gravitational waves from unknown isolated sources and Scorpius X-1: Results from the second LIGO science run". Physical Review D. 76 (8): 082001. arXiv:gr-qc/0605028. Bibcode:2007PhRvD..76h2001A. doi:10.1103/PhysRevD.76.082001. S2CID 209843313.
  40. "Searching for the youngest neutron stars in the galaxy". LIGO Scientific Collaboration. Retrieved 28 November 2015.
  41. Binétruy, Pierre; Bohé, Alejandro; Caprini, Chiara; Dufaux, Jean-François (13 June 2012). "Cosmological backgrounds of gravitational waves and eLISA/NGO: phase transitions, cosmic strings and other sources". Journal of Cosmology and Astroparticle Physics. 2012 (6): 027. arXiv:1201.0983. Bibcode:2012JCAP...06..027B. doi:10.1088/1475-7516/2012/06/027. S2CID 119184947.
  42. Damour, Thibault; Vilenkin, Alexander (2005). "Gravitational radiation from cosmic (super)strings: Bursts, stochastic background, and observational windows". Physical Review D. 71 (6): 063510. arXiv:hep-th/0410222. Bibcode:2005PhRvD..71f3510D. doi:10.1103/PhysRevD.71.063510. S2CID 119020643.
  43. Mack, Katie (2017-06-12). "Black Holes, Cosmic Collisions and the Rippling of Spacetime". Scientific American (blogs).
  44. Schutz, Bernard F (21 June 2011). "Networks of gravitational wave detectors and three figures of merit". Classical and Quantum Gravity. 28 (12): 125023. arXiv:1102.5421. Bibcode:2011CQGra..28l5023S. doi:10.1088/0264-9381/28/12/125023. S2CID 119247573.
  45. Hu, Wayne; White, Martin (1997). "A CMB polarization primer". New Astronomy. 2 (4): 323–344. arXiv:astro-ph/9706147. Bibcode:1997NewA....2..323H. doi:10.1016/S1384-1076(97)00022-5. S2CID 11977065.
  46. Kamionkowski, Marc; Stebbins, Albert; Stebbins, Albert (1997). "Statistics of cosmic microwave background polarization". Physical Review D. 55 (12): 7368–7388. arXiv:astro-ph/9611125. Bibcode:1997PhRvD..55.7368K. doi:10.1103/PhysRevD.55.7368. S2CID 14018215.
  47. "PLANNING FOR A BRIGHT TOMORROW: PROSPECTS FOR GRAVITATIONAL-WAVE ASTRONOMY WITH ADVANCED LIGO AND ADVANCED VIRGO". LIGO Scientific Collaboration. Retrieved 31 December 2015.
  48. Price, Larry (September 2015). "Looking for the Afterglow: The LIGO Perspective" (PDF). LIGO Magazine (7): 10. Retrieved 28 November 2015.
  49. See Cutler & Thorne 2002, sec. 2.
  50. See Cutler & Thorne 2002, sec. 3.
  51. See Seifert F., et al. 2006, sec. 5.
  52. See Golm & Potsdam 2013, sec. 4.

Further reading
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.